Erik ten Hag’s side have been looking to reinforce their midfield all summer and the PA news agency understands a deal worth an initial 60million euros (£50.7m) is close for the Brazil international.
The fee for Casemiro could rise to 70m euros (£59.2m) if clauses are met, with a four-year deal plus the option of a further season on the table.
Ten Hag said he “cannot tell anything” when asked about the Brazil international in United’s press conference on Friday, but Madrid boss Ancelotti was more forthcoming when speaking to the media in Spain.
“I’ve discussed it with him this morning,” the Italian said. “He wants to try a new challenge, a new opportunity.
“The club understand it. With all he’s done for this club and the person he is, we have to respect it.
“There are talks right now, he’s still a Real Madrid player at this stage, but he wants to leave. If he goes, we have the resources to replace him.
“I haven’t tried to convince him, I just listened, because I have spoken to Casemiro throughout my time here and he has helped us so much. Having heard what he wants, there’s no way back.
“If he doesn’t stay, we’ll have an enormous sense of gratitude to him for all he’s done. We have replacements within the squad.
“(Aurelien) Tchouameni was signed for this position and he’s one of the best central midfielders on the market right now, then we’ve got (Toni) Kroos, who can play in that position too, just like he did in my second year here, and there’s (Eduardo) Camavinga as well”.
Casemiro – a former team-mate of Cristiano Ronaldo and Raphael Varane in Spain – is a five-time Champions League winner with Madrid, who he joined from Sao Paulo in his homeland in 2013.